Short, Ian
(2006).
**K**(1|*b _{n}*).

*Annales Academiae Scientiarum Fennicae Mathematica*, 31(2) pp. 315–327.

(Accepted Manuscript)
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URL: | http://www.emis.ams.org/journals/AASF/Vol31/short.... |
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## Abstract

The Stern-Stolz theorem states that if the infinite series ∑|*b _{n}*| converges, then the continued fraction

**K**(1|

*b*) diverges. H. S. Wall asks whether just convergence, rather than absolute convergence of ∑

_{n}*b*is sufficient for the divergence of

_{n}**K**(1|

*b*). We investigate the relationship between ∑|

_{n}*b*| and

_{n}**K**(1|

*b*) with hyperbolic geometry and use this geometry to construct a sequence

_{n}*b*of real numbers for which both ∑|

_{n}*b*| and

_{n}**K**(1|

*b*) converge, thereby answering Wall's question.

_{n}Item Type: | Journal Item |
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Copyright Holders: | 2006 The Author |

ISSN: | 1239-629X |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 22452 |

Depositing User: | Ian Short |

Date Deposited: | 29 Jul 2010 10:47 |

Last Modified: | 06 Oct 2016 04:49 |

URI: | http://oro.open.ac.uk/id/eprint/22452 |

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